Given $ m \angle MON = 9x + 16$, $ m \angle LOM = 2x + 39$, and $ m \angle LON = 66$, find $m\angle LOM$. $O$ $L$ $N$ $M$
Explanation: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Substitute in the expressions that were given for each measure: $ {2x + 39} + {9x + 16} = {66}$ Combine like terms: $ 11x + 55 = 66$ Subtract $55$ from both sides: $ 11x = 11$ Divide both sides by $11$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $m\angle LOM$ $ m\angle LOM = 2({1}) + 39$ Simplify: $ {m\angle LOM = 2 + 39}$ So ${m\angle LOM = 41}$.